Generalizations of Popoviciu's and Bellman's Inequalities

摘要

In the paper, we generalize the well-known Bellman's and Popoviciu's inequalities, and get new Bellman's and Popoviciu's type inequalities. These new results provide new estimates on inequalities of these type. As application, we establish a Minkowski inequality, which in special case yields the well-known dual Minkowski inequality for volumes difference.